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Title: A High-Order Accurate Parallel Solver for Maxwell's Equations on Overlapping Grids

Abstract

A scheme for the solution of the time dependent Maxwell's equations on composite overlapping grids is described. The method uses high-order accurate approximations in space and time for Maxwell's equations written as a second-order vector wave equation. High-order accurate symmetric difference approximations to the generalized Laplace operator are constructed for curvilinear component grids. The modified equation approach is used to develop high-order accurate approximations that only use three time levels and have the same time-stepping restriction as the second-order scheme. Discrete boundary conditions for perfect electrical conductors and for material interfaces are developed and analyzed. The implementation is optimized for component grids that are Cartesian, resulting in a fast and efficient method. The solver runs on parallel machines with each component grid distributed across one or more processors. Numerical results in two- and three-dimensions are presented for the fourth-order accurate version of the method. These results demonstrate the accuracy and efficiency of the approach.

Authors:
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
907845
Report Number(s):
UCRL-JRNL-215684
TRN: US200721%%418
DOE Contract Number:  
W-7405-ENG-48
Resource Type:
Journal Article
Journal Name:
SIAM Journal of Scientific Computing, vol. 28, no. 5, October 20, 2006, pp. 1730-1765
Additional Journal Information:
Journal Volume: 28; Journal Issue: 5
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUMM MECHANICS, GENERAL PHYSICS; 42 ENGINEERING; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ACCURACY; APPROXIMATIONS; BOUNDARY CONDITIONS; EFFICIENCY; IMPLEMENTATION; LAPLACIAN; VECTORS; WAVE EQUATIONS

Citation Formats

Henshaw, W D. A High-Order Accurate Parallel Solver for Maxwell's Equations on Overlapping Grids. United States: N. p., 2005. Web.
Henshaw, W D. A High-Order Accurate Parallel Solver for Maxwell's Equations on Overlapping Grids. United States.
Henshaw, W D. 2005. "A High-Order Accurate Parallel Solver for Maxwell's Equations on Overlapping Grids". United States. https://www.osti.gov/servlets/purl/907845.
@article{osti_907845,
title = {A High-Order Accurate Parallel Solver for Maxwell's Equations on Overlapping Grids},
author = {Henshaw, W D},
abstractNote = {A scheme for the solution of the time dependent Maxwell's equations on composite overlapping grids is described. The method uses high-order accurate approximations in space and time for Maxwell's equations written as a second-order vector wave equation. High-order accurate symmetric difference approximations to the generalized Laplace operator are constructed for curvilinear component grids. The modified equation approach is used to develop high-order accurate approximations that only use three time levels and have the same time-stepping restriction as the second-order scheme. Discrete boundary conditions for perfect electrical conductors and for material interfaces are developed and analyzed. The implementation is optimized for component grids that are Cartesian, resulting in a fast and efficient method. The solver runs on parallel machines with each component grid distributed across one or more processors. Numerical results in two- and three-dimensions are presented for the fourth-order accurate version of the method. These results demonstrate the accuracy and efficiency of the approach.},
doi = {},
url = {https://www.osti.gov/biblio/907845}, journal = {SIAM Journal of Scientific Computing, vol. 28, no. 5, October 20, 2006, pp. 1730-1765},
number = 5,
volume = 28,
place = {United States},
year = {Fri Sep 23 00:00:00 EDT 2005},
month = {Fri Sep 23 00:00:00 EDT 2005}
}